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Popular >

simplify ln(x^2)-2ln(sqrt(x))

Solution

simplify

ln (x^{2}) - 2 ln (x)

Solution

ln (x)

Solution steps

ln (x^{2}) - 2 ln (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (x) = ln ((x)^{2})

= ln (x^{2}) - ln ((x)^{2})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x^{2}) - ln ((x)^{2}) = ln (\frac{x ^{2}}{( x ) ^{2}})

= ln (\frac{x ^{2}}{( x ) ^{2}})

Simplify

\frac{x ^{2}}{( x ) ^{2}} : x

= ln (x)

Popular Examples

simplify 2ln((sqrt(2))/2)simplify

2 ln (\frac{2}{2})

expand log_{4}(16a)expand

lo g_{4} (16 a)

simplify 2log_{10}(5)+5log_{10}(x)simplify

2 lo g_{10} (5) + 5 lo g_{10} (x)

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simplify log_{b}(1/y)simplify

lo g_{b} (\frac{1}{y})

Frequently Asked Questions (FAQ)

What is ln(x^2)-2ln(sqrt(x)) ?
The solution to ln(x^2)-2ln(sqrt(x)) is ln(x)